We have calculated a grid of massive star wind models and mass-loss rates for a wide range of metal abundances between 1 / 100 \leq Z / \mbox { $Z _ { \odot } $ } \leq 10 .

The calculation of this grid completes the Vink et al .
( 2000 ) mass-loss recipe with an additional parameter Z .
We have found that the exponent of the power law dependence of mass loss vs. metallicity is constant in the range between 1/30 \leq Z / \mbox { $Z _ { \odot } $ } \leq 3 .
The mass-loss rate scales as \dot { M } \propto Z ^ { 0.85 } \mbox { $v _ { \infty } $ } ^ { p } with p = -1.23 for stars with \mbox { $T _ { eff } $ } \ga 25 ~ { } 000 K , and p = -1.60 for the B supergiants with \mbox { $T _ { eff } $ } \la 25 ~ { } 000 K. Taking also into account the metallicity dependence of v _ { \infty } , using the power law dependence \mbox { $v _ { \infty } $ } \propto Z ^ { 0.13 } from Leitherer et al .
( 1992 ) , the overall result of mass loss as a function of metallicity can be represented by \dot { M } \propto Z ^ { 0.69 } for stars with \mbox { $T _ { eff } $ } \ga 25 ~ { } 000 K , and \dot { M } \propto Z ^ { 0.64 } for B supergiants with \mbox { $T _ { eff } $ } \la 25 ~ { } 000 K .

Although it is derived that the exponent of the mass loss vs. metallicity dependence is constant over a large range in Z , one should be aware of the presence of bi-stability jumps at specific temperatures .
Here the character of the line driving changes drastically due to recombinations of dominant metal species resulting in jumps in the mass loss .
We have investigated the physical origins of these jumps and have derived formulae that combine mass loss recipes for both sides of such jumps .
As observations of different galaxies show that the ratio Fe/O varies with metallicity , we make a distinction between the metal abundance Z derived on the basis of iron or oxygen lines .

Our mass-loss predictions are successful in explaining the observed mass-loss rates for Galactic and Small Magellanic Cloud O-type stars , as well as in predicting the observed Galactic bi-stability jump .
Hence , we believe that our predictions are reliable and suggest that our mass-loss recipe be used in future evolutionary calculations of massive stars at different metal abundance .
A computer routine to calculate mass loss is publicly available .